I have been using NASA's Program to Optimize Simulated Trajectories (POST) for developing a 3 DoF trajectory optimization code for ascent launch vehicle flight to orbit. The dynamics are integrated in Earth-Centered Inertial (ECI) frame where the thrust acceleration vector and the drag acceleration vector are modelled in Body (B) frame and transformed to ECI frame while the gravity acceleration vector is given in ECI frame directly. My understanding is that the B frame and geographic (G) frame (commonly known as North-East-Down frame) are rotating reference frames in contrast to ECI.
The transformation between B and G frames are clear however for going from G to ECI or vice versa there has been some unidentified hiccups particularly for the acceleration vector transformation from B frame (to go to ECI frame) and relative velocity vector transformation from ECI (to go to B frame)
With this background, my questions are:
Conventional knowledge says that for a vertically launched vehicle, the relative flight path angle (in G frame) should be 90 degree during vertical flight i.e. relative velocity vector in G-frame should be non-nulled in only one component. However, it is not so based on the above preliminaries, what might be the cause for this?
Is there a particular component missing in the transformation of the thrust acceleration vector from G frame to ECI frame, besides the transformation matrix itself?